In this paper we consider mappings

which map the binary operation symbol f to the term

(f) which do not necessarily preserve the arities. We call these mappings generalized hypersubstitutions. Any generalized hypersubstitution

can be extended to a mapping

on the set of all terms of type

= (2). We de ne a binary operation on the set

(2) of all generalized hypersubstitutions of type

= (2) by using this extension The set

(2) together with the identity generalized hypersubstitution

which maps f to the term f(

) forms a monoid. We determine all regular elements of this monoid.